Mass Transport Problem Research Articles

Nanophotocatalysis using nanoparticles of titania: Mineralization and finite element modelling of Solophenyl dye decolorization

This paper investigates the mineralization and numerical finite element model for simulation of decolorization of Solophenyl Red 3BL (SR) by nanophotocatalysis using immobilized titania nanoparticle. A simple and effective method was developed for the immobilization of titania nanoparticles. UV–vis, ion chromatography (IC) and total organic carbon (TOC) analyses were employed to obtain the details of the photocatalytic decolorization and mineralization of SR. The nitrate and sulfate anions were detected as photocatalytic mineralization products of SR. Ninety-two percent total organic carbon can be eliminated after 240 min of irradiation time.The SEEP/W model was incorporated into the CTRN/W model and modified to solve mathematical equation describing decolorization process. The numerical model was first calibrated with an analytical equation for a simple mass transport problem through groundwater flow system. The simulation results were then compared to those results obtained from an experimental test for the decolorization of SR by nanophotocatalysis process and close agreement was achieved.

Stokes flow in ellipsoidal geometry

Particle-in-cell models for Stokes flow through a relatively homogeneous swarm of particles are of substantial practical interest, because they provide a relatively simple platform for the analytical or semianalytical solution of heat and mass transport problems. Despite the fact that many practical applications involve relatively small particles (inorganic, organic, biological) with axisymmetric shapes, the general consideration consists of rigid particles of arbitrary shape. The present work is concerned with some interesting aspects of the theoretical analysis of creeping flow in ellipsoidal, hence nonaxisymmetric domains. More specifically, the low Reynolds number flow of a swarm of ellipsoidal particles in an otherwise quiescent Newtonian fluid, that move with constant uniform velocity in an arbitrary direction and rotate with an arbitrary constant angular velocity, is analyzed with an ellipsoid-in-cell model. The solid internal ellipsoid represents a particle of the swarm. The external ellipsoid contains the ellipsoidal particle and the amount of fluid required to match the fluid volume fraction of the swarm. The nonslip flow condition on the surface of the solid ellipsoid is supplemented by the boundary conditions on the external ellipsoidal surface which are similar to those of the sphere-in-cell model of Happel (self-sufficient in mechanical energy). This model requires zero normal velocity component and shear stress. The boundary value problem is solved with the aim of the potential representation theory. In particular, the Papkovich–Neuber complete differential representation of Stokes flow, valid for nonaxisymmetric geometries, is considered here, which provides the velocity and total pressure fields in terms of harmonic ellipsoidal eigenfunctions. The flexibility of the particular representation is demonstrated by imposing some conditions, which made the calculations possible. It turns out that the velocity of first degree, which represents the leading term of the series, is sufficient for most engineering applications, so long as the aspect ratios of the ellipsoids remains within moderate bounds. Analytical expressions for the leading terms of the velocity, the total pressure, the angular velocity, and the stress tensor fields are obtained. Corresponding results for the prolate and the oblate spheroid, the needle and the disk, as well as for the sphere are recovered as degenerate cases. Novel relations concerning the ellipsoidal harmonics are included in the Appendix.

Simultaneous saccharification and fermentation of steam-pretreated barley straw at low enzyme loadings and low yeast concentration

The maximum concentration of water-insoluble solids (WIS) in simultaneous saccharification and fermentation (SSF) is restricted due to inhibition of the enzymes and the yeast, as well as mass transport problems caused by the viscosity of the pretreated material. However, the higher the concentration of WIS during SSF the less energy is needed in the subsequent distillation and evaporation steps. In this study, SSF was performed on barley straw sprayed with H 2SO 4 and steam pretreated at conditions yielding a highly digestible material, aiming to increase the WIS concentration and decrease the enzyme loading and the yeast concentration in SSF, in order to reduce the production cost. Three concentrations of WIS (5, 7.5 and 10%), and three enzyme loadings (5, 10 and 20 FPU/g cellulose) of Celluclast 1.5 L complemented with Novozym 188 were investigated in terms of ethanol yield. Ordinary cultivated Baker's yeast and Baker's yeast cultivated on barley straw hydrolyzate were also evaluated in terms of ethanol yield. The highest ethanol yield, 82% of the theoretical based on the glucose content in barley straw, was obtained after SSF with 5% WIS at an enzyme loading of 20 FPU/g cellulose together with 5 g/L ordinary cultivated yeast. Increased WIS concentration and decreased enzyme loading decreased the ethanol yield. However, by cultivating the yeast in hydrolyzate from pretreated barley straw the WIS concentration in SSF could be increased from 5% to 7.5% and the yeast concentration could be reduced from 5 to 2 g/L, while still attaining a yield of approximately 80%.

Minimal measures, one-dimensional currents and the Monge–Kantorovich problem

In recent works L.C. Evans has noticed a strong analogy between Mather's theory of minimal measures in Lagrangian dynamic and the theory developed in the last years for the optimalmass transportation (or Monge–Kantorovich) problem. In this paper we start to investigate this analogy by proving that to each minimal measure it is possible to associate, in a natural way, a family of curves on the space of probability measures. These curves are absolutely continuous with respect to the metric structure related to the optimal mass transportation problem. Someminimality properties of such curves are also addressed.

Numerical modelling and laboratory studies on the removal of Direct Red 23 and Direct Red 80 dyes from textile effluents using orange peel, a low-cost adsorbent

Wastewater containing direct dyes discharged from various industries, in particular, textile industry often causes many environmental problems. Considering the possibility of the adsorption process of synthetic dyes and their removal from aqueous solutions using orange peel as an eco-friendly and low-cost adsorbent before discharging to the receiving environment is the most important task. This paper presents a numerical finite element model to simulate the removal of dissolved textile synthetic dyes from wastewater taking into consideration both linear and the Langmuir isotherms to describe adsorption process. The CTRN/W model was integrated with SEEP/W model and modified to solve mathematical equations describing the problem at hand. The modelling accuracy was first verified with an analytical equation for a reactive mass transport problem including advection, dispersion and linear adsorption processes through groundwater flow medium. The modelling results were then compared to those results obtained from experimental tests for the removal of Direct Red 23 and Direct Red 80 dyes from textile wastewater using orange peel adsorbent. The model predictions somewhat agree with the experimental measurements. It was found that the adsorption process by orange peel adsorbent could be well described by the Langmuir isotherm. Furthermore, a pseudo-second order kinetics showed to be well-suited with the rate of sorption. Although the generation of such wastewater by the different industries is nearly unavoidable, the results of model presented here can help to design an appropriate environmental management strategy to minimise the adverse impacts caused by industrial wastewater.

Channel Flow Configuration for Studying the Kinetics of Surfactant−Polyelectrolyte Binding

A novel channel flow configuration was developed and utilized for studying the poly(styrenesulfonate)-cetylpyridinium ion interaction kinetics. The surfactant solution was continuously injected into a flow of polyelectrolyte solution, and the extent of the association reaction was probed at an ion-selective detector electrode. The system was modeled within an analytical approximation, which was tested by a finite-element simulation of the full convective mass transport problem including the homogeneous complexation reaction. The results show that association kinetics can be resolved and that the initial steps of the reaction are not influenced by intermolecular interactions between the bound surfactants. The presented methodology is general, and further development should enable the study of complex cooperative kinetics of surfactant-polyelectrolyte systems.

Equivalence between some definitions for the optimal mass transport problem and for the transport density on manifolds

In this paper we consider three problems, which are related to the classical Monge’s optimal mass transport problem and which are known to be equivalent when the ambient space is an open, convex and bounded subset of ℝn; to these problems there correspond different definitions of particular measures (often called transport densities), which are also known to be equivalent. Here we will generalize the setting of these problems and the resulting definitions of transport densities to the case of a Riemannian manifold endowed with a finslerian semidistance, and we will see that the equivalences still hold.

Transport density in Monge-Kantorovich problems with Dirichlet conditions

We study the properties of the transport density measure in the Monge-Kantorovich optimal mass transport problem in the presence of so-called Dirichlet constraint, i.e. when some closed set is given along which the cost of transportation is zero. The Hausdorff dimension estimates, as well as summability and higher regularity properties of the transport density are studied. The uniqueness of the transport density is proven in the case when the masses to be transported are represented by measures absolutely continuous with respect to the Lebesgue measure.

Optimal networks for mass transportation problems

In the framework of transport theory, we are interested in the following optimization problem: given the distributions µ+ of working people and µ- of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of µ+ from µ- with respect to a metric which depends on the transportation network.

Characterization of Batch-Microfabricated Scanning Electrochemical-Atomic Force Microscopy Probes

A procedure for the batch microfabrication of scanning electrochemical-atomic force microscopy (SECM-AFM) probes is described. The process yields sharp AFM tips, incorporating a triangular-shaped electrode (base width 1 microm, height 0.65 microm) at the apex. Microfabrication was typically carried out on (1)/(4) 3-in. wafers, yielding 60 probes in each run. The measured spring constant of the probes was in the range 1-1.5 N m(-1). To date, processing has been carried out twice successfully, with an estimated success rate for the fabrication process in excess of 80%, based on field emission-scanning electron microscopy imaging of all probes and current-voltage measurements on a random selection of approximately 30 probes. Steady-state voltammetric measurements for the reduction of Ru(NH(3))(6)(3+) in aqueous solution indicate that the electrode response is well-defined, reproducible, and quantitative, based on a comparison of the experimental diffusion-limited current with finite element simulations of the corresponding mass transport (diffusion) problem. Topographical imaging of a sputtered Au film with the SECM-AFM probes demonstrates lateral resolution comparable to that of conventional Si(3)N(4) AFM probes. Combined electrochemical-topographical imaging studies have been carried out on two model substrates: a 10-microm-diameter disk ultramicroelectrode (UME) and an array of 1-microm-diameter UMEs, spaced 12.5 microm apart (center to center). In both cases, an SECM-AFM probe was first employed to image the topography of the substrates. The tip was then moved back a defined distance from the surface and use to detect Ru(NH(3))(6)(2+) produced at the substrate, biased at a potential to reduce Ru(NH(3))(6)(3+), present in bulk solution, at a diffusion-controlled rate (substrate generation-tip collection mode). These studies establish the success of the batch process for the mass microfabrication of SECM-AFM tips.

Modelling Approach for Planar Self‐Breathing PEMFC and Comparison with Experimental Results

AbstractThis paper presents a model‐based analysis of a proton exchange membrane fuel cell (PEMFC) with a planar design as the power supply for portable applications.The cell is operated with hydrogen and consists of an open cathode side allowing for passive, self‐breathing, operation. This planar fuel cell is fabricated using printed circuit board (PCB) technology. Long‐term stability of this type of fuel cell has been demonstrated.A stationary, two‐dimensional, isothermal, mathematical model of the planar fuel cell is developed. Fickian diffusion of the gaseous components (O2, H2, H2O) in the gas diffusion layers and the catalyst layers is accounted for. The transport of water is considered in the gaseous phase only. The electrochemical reactions are described by the Tafel equation. The potential and current balance equations are solved separately for protons and electrons. The resulting system of partial differential equations is solved by a finite element method using FEMLAB (COMSOL Inc.) software.Three different cathode opening ratios are realized and the corresponding polarization curves are measured. The measurements are compared to numerical simulation results. The model reproduces the shape of the measured polarization curves and comparable limiting current density values, due to mass transport limitation, are obtained.The simulated distribution of gaseous water shows that an increase of the water concentration under the rib occurs. It is concluded that liquid water may condense under the rib leading to a reduction of the open pore space accessible for gas transport. Thus, a broad rib not only hinders the oxygen supply itself, but may also cause additional mass transport problems due to the condensation of water.

The specific features of the evolution of the viscous protoplanetary circumsolar disk

The problem of angular-momentum and mass transport in the disk is discussed and the disk viscosity is estimated. The evolution of the gas-dust protoplanetary disk at the stage of its formation inside the protostellar (protosolar) accretion envelope is considered. The conditions for the radial growth of the disk are estimated. For the subsequent period, when the central star (young Sun) is in the T Tauri phase, the temporal variations of the radius, mass, and the surface density of the disk, as well as the total mass flux from the disk onto the star (Sun), i.e., the mass accretion rate, are evaluated. The constraints on the initial value of the angular momentum of the protoplanetary circumsolar disk (that is, on the angular momentum of the protosolar cloud) are discussed with due regard for cosmochemical data.

Concentration fields in evaporating droplets

An analytical solution of the problem of diffusional mass transport inside a spherical binary mixture droplet is presented. The droplet evaporates according to the d 2-law. Mass fraction profiles of the mixture components are obtained as series expansions in confluent hypergeometric, Legendre and sine/cosine functions. The analytical description is valid for arbitrary ratio of the rate of shrinkage of the sphere surface to the diffusion coefficient in the liquid phase. The results allow for a prediction of the morphology of the dried particles, i.e., whether hollow or solid spheres result from the drying process. The field of application of the results presented is spray drying of solutions of solid substances.

Linear morphological stability analysis of the solid-liquid interface in rapid solidification of a binary system.

The interface stability against small perturbations of the planar solid-liquid interface is considered analytically in linear approximation. Following the analytical procedure of Trivedi and Kurz [Acta Metall. 34, 1663 (1986)]], which is advancing the original treatment of morphological stability by Mullins and Sekerka [J. Appl. Phys. 35, 444 (1964)]] to the case of rapid solidification, we extend the model by introducing the local nonequilibrium in the solute diffusion field around the interface. A solution to the heat- and mass-transport problem around the perturbed interface is given in the presence of the local nonequilibrium solute diffusion. Using the developing local nonequilibrium model of solidification, the self-consistent analysis of linear morphological stability is presented with the attribution to the marginal (neutral) and absolute morphological stability of a rapidly moving interface. Special consideration of the interface stability for the cases of solidification in negative and positive thermal gradients is given. A quantitative comparison of the model predictions for the absolute morphological stability is presented with regard to experimental results of Hoglund and Aziz [D. E. Hoglund and M. J. Aziz, in Kinetics of Phase Transformations, edited by M.O. Thompson, M. J. Aziz, and G. B. Stephenson, MRS Symposia Proceedings No. 205 (Materials Research Society, Pittsburgh, 1991), p. 325] on critical solute concentration for the interface breakdown during rapid solidification of Si-Sn alloys.

Interrelation between Papkovich-Neuber and Stokes general solutions of the stokes equations in spheroidal geometry

Many practical applications involve particles (inorganic, organic, biological) with non-spherical but still axisymmetric shapes. The present work is concerned with some interesting aspects of the theoretical analysis of Stokes flow in spheroidal domains. Two different complete representations of Stokes flow are considered here. The first one is obtained through the theory of generalized eigenfunctions, according to which the stream function is expanded in terms of separable and semiseparable eigenfunctions. The second one, valid in non-axisymmetric geometries as well, is the Papkovich-Neuber differential representation, where the velocity and pressure fields are expressed in terms of harmonic spheroidal eigenfunctions. Connection formulae are obtained for the case of axisymmetric flows, which relate the spheroidal harmonic eigenfunctions of the Papkovich-Neuber representation with the semiseparable spheroidal stream eigenfunctions. In the case of axisymmetric spheroidal flows the Papkovich-Neuber approach is equivalent to the Stokes stream function approach, but the three-dimensional representation offers certain important advantages. Particle-in-cell models for Stokes flow through a swarm of particles are of substantial practical interest, because they provide a relatively simple platform for the analytical or semianalytical solution of heat and mass transport problems. The early versions of these models were concerned with spherical particles. For this reason particle-in-cell models for spheroidal particles were developed more recently. The flexibility of the Papkovich-Neuber differential representation is demonstrated by solving the problem of the flow in a fluid cell filling the space between two confocal spheroidal surfaces with Kuwabara-type boundary conditions.

Model of adsorption–reaction–desorption in a swarm of spheroidal particles

AbstractThe mass transport problem from a Newtonian fluid to a swarm of prolate or oblate spheroidal adsorbing particles under creeping flow conditions is considered here. The spheroidal‐in‐cell model is used for the analytical description of the flow field within the swarm. A realistic adsorption–reaction–desorption mechanism is used to describe the adsorption of mass on the particle surface, instead of the assumption of instantaneous adsorption that has been adopted previously. The convective diffusion equation accompanied by the appropriate boundary conditions is solved analytically for the case of high Peclet numbers and numerically for the low ones. In both cases, analytical expressions for the overall Sherwood number, the adsorption rate, and the mass transport coefficient were obtained. It was found that the adsorption rate is higher for oblate shapes and for diffusional, instead of convectional, environments. Finally, the assumption of instantaneous adsorption leads to values for the overall Sherwood number and the adsorption efficiency that are 15–50% lower and 10–35% higher, respectively, than those obtained by using the more realistic adsorption–reaction–desorption model. © 2004 American Institute of Chemical Engineers AIChE J, 50: 779–785, 2004

Mass transport in gravity waves revisited

On re‐examining the problem of mass transport due to partially standing waves in a domain that can be closed or open ended, it is pointed out that several aspects of the existing theories need to be clarified. Particular attention is paid to the free surface setup, whose expression is shown to be different when described by the Eulerian and Lagrangian approaches. In the Lagrangian system, it is the horizontal gradient of the setup, rather than the mean pressure gradient alone, that is implied by the condition of no net flux in a closed domain. In connection with this, one may determine for an unbounded domain the streamline value along the free surface, which cannot be fixed in the stream function formulation alone, by requiring the setup due to the unidirectional part of the mass transport to be zero. Three components of the free surface setup, which are of different orders of magnitude and arise owing to various mechanisms, are obtained in the process of deriving the solutions for the mass transport velocity in the boundary layers and the fluid core.

Numerical simulation of a disk-type SOFC for impedance analysis under power generation

To support the impedance analysis in a disk-type SOFC under power generation, a numerical simulation procedure, whose simulation outputs the total impedance of an actual-size disk-type SOFC cell for the input of the local impedance of cell, has been proposed. In the simulation, the quasi-one-dimensional radial flow and mass transport problem with cell reactions is solved. Transient distributions of electromotive force, current and concentrations of chemical species in the cell are calculated to obtain the total cell impedance with parameters, such as local impedance of the cell, ac frequency, fuel utilization, gas flow rate, etc. A parametric simulation study for the simplest case under typical experimental conditions has been carried out. It is found that the Cole–Cole plot for the total cell impedance shows a capacitive semicircle, even if a pure resistance is assumed as the local impedance of the cell. The diameter of the impedance semicircle changes with fuel utilization and supplied gas flow rate, being affected by the diffusion in the flow direction. The characteristic frequency of the impedance semicircle depends on the transit time of the gas through the cell which is also affected by the diffusion in the flow direction. It is also suggested that the total cell impedance appears as a convolution of this capacitive semicircle impedance and local impedance of the cell.

Reconstruction of the early Universe as a convex optimization problem

We show that the deterministic past history of the Universe can be uniquely reconstructed from knowledge of the present mass density field, the latter being inferred from the three-dimensional distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias. Reconstruction ceases to be unique below those scales – a few Mpc – where multistreaming becomes significant. Above 6 h−1 Mpc we propose and implement an effective Monge–Ampere–Kantorovich method of unique reconstruction. At such scales the Zel'dovich approximation is well satisfied and reconstruction becomes an instance of optimal mass transportation, a problem which goes back to Monge. After discretization into N point masses one obtains an assignment problem that can be handled by effective algorithms with not more than O(N3) time complexity and reasonable CPU time requirements. Testing against N-body cosmological simulations gives over 60 per cent of exactly reconstructed points. We apply several interrelated tools from optimization theory that were not used in cosmological reconstruction before, such as the Monge–Ampere equation, its relation to the mass transportation problem, the Kantorovich duality and the auction algorithm for optimal assignment. A self-contained discussion of relevant notions and techniques is provided.

Numerical resolution of an “unbalanced” mass transport problem

We introduce a modification of the Monge–Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented Lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.